Electronic structure modelling of the edge-functionalisation of graphene by Mn_xO_y particles

Abstract

The use of graphenic carbon is attractive as a basal or intermediate support for catalytic particles in advanced catalytic electrodes. This popularity is motivated by its excellent electrical properties and ability to form foliated conformal coatings of exceptional surface area and flexibility. Surface- and edge-functionalisation of graphene sheets affords diverse routes to the covalent attachment of candidate catalytic species. Of particular interest to advanced water oxidation is the possibility of covalent attachment of Mn_xO_y species partially recapitulating the chemistry of the Mn₄O₅Ca active site of Photosystem II (PSII), which achieves the four-electron oxidation of water under physiological conditions. Here, we report aperiodic density functional theory (DFT) investigations of candidate attachment geometries for a variety of manganese oxide particles to graphene sheets. We find that the flexibility of graphene sheets as well as the conformational degrees of freedom of candidate edge functionalisation permits a large variety of realistic attachment geometries that can act as attachment sites for molecular manganese-oxide species or nuclei for the growth of periodic manganese oxides. We find that substantially simplified models of graphene attachment afford an excellent compromise between computational efficiency, tractability, and accuracy, and characterise the accuracy of these models in detail.

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1 Introduction

Graphene is an atomic monolayer of graphite comprised of a hexagonal periodic 2D lattice of sp²-hybridised carbon atoms, with an idealised nearest-neighbour C–C distance of 142 pm.^1,2 Graphene has a range of superlative physical properties, including an exceptional Young's modulus (≈1.0 TPa) making it one of the strongest materials known,³ very high specific surface area (theoretically up to 2630 m² g⁻¹),‡ exceptional thermal conductivity,⁶ and unique optical and electron transport behaviour.^2,7–9

Graphene and its derivatives are attractive as a basal or intermediate component of high-performance electrodes because of their excellent electrical conductivity and ability to form a highly foliated and flexible conformal coating on other substrates. These properties facilitate the creation of electrodes with very high electrochemically sensible surface areas for use in catalysis,^10–12 sensors,^13–15 supercapacitors,^16–21 and metal ion batteries.^14,22,23 The Hummers process and its modifications^24,25 effect the chemical exfoliation of graphite to graphene oxide (GO), which may then be partially reduced to obtain reduced graphene oxide (rGO) by chemical,^19,26–28 thermal,²⁹ or photolytic reduction.^30,31 However, GO produced by the Hummers process is substantially defective with respect to pristine graphene, typically being heavily topologically damaged and refunctionalised with carboxylic acid, epoxide, hydroxide, and ketone moieties at both surfaces and edges.^32,33 Reduction to rGO imperfectly recovers some of the desirable properties of unmodified graphene, including improvement in electrical conductivity.^30,33,34 However, multiple routes to bulk graphene exist, including bottom-up synthesis to obtain pristine graphene of regular dimensions,³⁵ unzipping of carbon nanotubes (CNTs),³⁶ and mechanical delamination of graphite to obtain pristine monolayers.⁹

A large number of publications report the association of metal oxide nanoparticles with graphene in various forms, to create materials with potential or actual synergistic electrochemical functionality. This functionality may be in the form of providing a high surface area and conductive support for charge carrier exchange with metal oxide particles, or by the creation of semiconductor heterojunctions.¹⁵ Moreover, the activation of graphene to catalytic reactivity by incorporation in metal oxide/graphene van der Waals heterostructures has been elucidated theoretically.³⁷ A representative sample of experimentally prepared oxo-metal/graphene composites are summarised in Table 1. A preponderance of associations between metal oxide nanoparticles and graphene sheets in the literature appear to be of a noncovalent nature, however some covalently attached particles are noted (e.g.ref. 38). Alternatively, precipitation of Mn₃O₄ particles with presumed high specificity to ionic functionalities is also known.¹⁰

Table 1 Representative sample of preparations of graphene derivatives in association with transition metal oxides. TMO: transition metal oxide, GO: graphene oxide, rGO: reduced graphene oxide, IL-rGO: reduced graphene oxide functionalised with ionic liquid moieties, ORR: oxygen reduction reaction, LED: light-emitting diode, aMEGO: activated microwave-expanded graphene oxide, ZIF-8: a zeolitic zinc imidazolate framework with the sodalite structure

Year	Method	Application	TMO identity	TMO disposition	Graphene disposition	Ref.
2008	Photoredox	Solar cell	TiO2	‘nanoparticles’	rGO	39
2009	Redox	Supercapacitor	SnO2	‘nanoparticles’	rGO	16
2009	Self-assembly	Lithium ion battery	SnO2	‘nanoparticles’	rGO	22
2010	Photoredox	rGO dispersion	H3PW12O40	Keggin cluster	rGO	28
2011	Electrostatic coprecip.	Supercapacitor	MnO2	‘nanosheets’	rGO	17
2011	Electrostatic coprecip.	ORR	Mn3O4	‘nanoparticles’	IL-rGO	10
2012	Carboxylate coord.	LED	ZnO	‘nanoparticles’	GO	38
2012	Reductive precipitation	Supercapacitor	MnO2	‘nanoparticles’	‘aMEGO’	40
2012	Self-assembly	Pollutant degradation	ZnO	‘nanoparticles’	rGO	11
2013	Mechanical milling	Supercapacitor	α-MnO2	‘nanorods/particles’	GO	18
2014	Several	Lithium ion battery	Mn3O4/MnO	‘nanoparticles’	GO/rGO	23
2015	Reductive precipitation	HCOOH dehydration	AuPd–MnOx	‘nanocomposite’	ZIF-8/rGO	12
2016	Aminosiloxane linkage	Microbicide	ZnO	‘nanoparticles’	GO	41
2017	Hydrothermal	Gas sensor	SnO2	‘nanorods’	rGO	14
2019	Electrodeposition	Supercapacitor	MnO2	‘nanosheets’	rGO	20
2020	Reductive precipitation	Supercapacitor	Mn3O4	‘nanoclusters’	rGO	42

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This work seeks to characterise bichelation of a number of notional Mn_xO_y clusters via edge-functionalised graphene (EFG) sheets. These clusters resemble known or potential water oxidation catalysts (WOCs), with similarity to the Mn₄O₅Ca oxygen evolving complex (OEC) of the Photosystem II (PSII) holoenzyme.⁴³ This complex effects the four-electron photo-driven oxidation of water, the first step of oxygenic photosynthesis in plants and cyanobacteria.⁴⁴ These clusters may represent molecular catalytic or procatalytic particles of definite nuclearity, or represent points of attachment of arbitrarily large TMO nanoparticles or nanosheets. We conceive of such attachment of TMO particles to graphene sheets as an essential component in the construction of notional hierarchically structured electrodes (HSEs) for water oxidation, which employ EFG as an intermediate electron transport system of exceptional surface area (illustrated in Fig. 1). Mn_xO_y/graphene composites for electrochemical applications have been reported with Mn_xO_y particles in a number of dispositions, including surfacially adsorbed ‘amorphous or poorly crystalline’ MnO₂ particles of diameter 2–3 nm,⁴⁰ adsorbed mesoporous Mn₃O₄ nanoclusters of diameter 2–20 nm,⁴² non-uniform aggregates of relatively monodisperse (9.45 ± 1.72 nm) Mn₃O₄ spheroids on functionalised rGO,¹⁰ precipitation of birnessite-like MnO₂ nanosheets (of a characteristic scale of hundreds of nanometers) in an electrostatic heterostructure with functionalised rGO,¹⁷ and electrostatic precipitation of ‘ultrahigh MnO₂[nanosheet] loading’ on a topologically complex rGO aerogel.²⁰ These examples attest to a diversity of Mn_xO_y stoichiometries, particle scales, dispersities, and aspect ratios which are accessible through a range of synthetic techniques.

Fig. 1 (a) Schematic depiction of hierarchically structured electrode composed of M_xO_y catalytic particles attached by edge functionalisation to graphene supports, which are in turn attached to a metal foam substrate. (b) Schematic depiction of catalytic activity at edge-attached manganese oxide particles. Electron transport from catalytic particles, through graphene sheet, into metal foam, is indicated with green arrows.

Amide coupling is an established method of derivatisation of carboxylic acid moieties produced graphene sheets (e.g.ref. 10, 45 and 46). Here we consider the attachment of Mn_xO_y particles to extended polycyclic aromatic hydrocarbons (PAHs) through the intermediation of amide moieties. These PAHs are intended to be representative of substructures of graphene sheets which have been selectively oxidised at their edges to produce carboxylic acid moieties, which are then condensed with 3- and 4-aminobenzoic acid to afford protrusive carboxylate ligands for coordination of oxo-manganese clusters. We hypothesised that the large number of conformational degrees of freedom afforded by typical amide functionalisation at graphene edges—as well as the intrinsic flexibility of graphene itself—would facilitate attachment of Mn_xO_y particles of a wide variety of shapes to a wide range of edge-functionalised graphene models. Manganese oxide clusters attached to graphene sheets may be construed either as molecular species of definite nuclearity, or as the attachment points for precipitation of large-scale periodic structures at nucleation sites provided by edge functionalisation of graphene.

Carboxylate residues are capable of coordinating transition metals as a monodentate, chelating, or bridging ligand. Therefore, carboxylate edge-functionalisation of graphene is anticipated to permit binding of metal oxide clusters in a wide variety of configurations (Fig. 2). The allowable binding configurations are controlled by a number of factors:

• Graphene sheets are liable to possess multiple geometrically distinct micro-environments at their perimeters, and edge-functionalisation of the graphene at these environments will yield salient carboxylate ligands more or less suited to coordinating metal oxide clusters of differing geometry.

• Carboxylate ligand identity informs the coordination geometries that are allowable for a given edge functionalisation pattern. Particularly, the length and flexibility of aliphatic chains present in the ligand is of capital importance.

• Differing metal oxide cluster topologies will facilitate differing modes of coordination by carboxylate ligands.

This work was undertaken to probe the energetic and geometric behaviour of a range of plausible edge functionalisation schemes, as well as to characterise the extent of electronic coupling between the TMO cluster and the EFG. In the case of coordination by a single ligand, attachment of a cluster to EFG is substantially conformationally unconstrained. However, chelation of a TMO cluster by two or more ligands will place constraints on the relative geometry of (a) the EFG sheet, (b) the points of attachment of the ligands, (c) the conformation of those ligands, and (d) the conformation of the TMO cluster. Therefore, we sought to estimate the energetics of binding TMO particles by bichelate attachment to EFG model edges and determine how the degrees of freedom present in the EFG–TMO cluster complexes contribute to these energetics.

Fig. 2 Schematic, non-exhaustive illustration of the diversity of potential bichelate attachment topologies connecting TMO clusters and nanosheets to graphene edges. (a) Carboxylate-terminated ligands of differing lengths and/or conformational flexibilites, capable of chelating a notional oxo-metal cluster or MM edges of a periodic nanosheet. (b) Chelation of a TMO cluster at a graphene edge by two different ligand types. (c) TMO attachment at a localised deformation of the edge of a graphene sheet. This deformation may be intrinsic or induced by forces arising from TMO cluster coordination. (d) Chelation of TMO clusters by ligands on distinct stacked graphene sheets. (e) Coordination of TMO clusters at a localised graphene microenvironment (a fold). (f) Coordination of a TMO between two disconnected graphene sheets.

Graphene is quite flexible, and experimentally characterised graphene is commonly very crumpled (see e.g.ref. 47). The stability of highly folded graphene implies that arbitrarily separated functional groups may participate in the chelation of a TMO cluster. Indeed, coordinating functional groups chelating a TMO cluster may be located on distinct graphene sheets. The flexibility of graphene over large scales and its interaction with edge functionalisation and coordination complexes cannot be directly assessed by the density functional theory methodology we have adopted, and therefore we measure the energy associated with small scale folding of a graphene edge to indirectly characterise the extent to which this degree of freedom may participate in stabilising TMO cluster chelation.

2 Methodology

2.1 Computational details

Calculations were performed in the ORCA 4 electronic structure suite⁴⁸ running on 64-bit Linux. Electronic structures were computed by spin-unrestricted density functional theory (DFT), using the Split-RI-J approximation to the Coulomb energy.⁴⁹ The exchange and correlation interactions were approximated by the combined functional of Becke and Perdew (BP86).^50,51 The Grimme3 dispersion correction (D3BJ) was applied to model the noncovalent dispersion interactions within the molecule.^52,53

Typically, geometry optimisations were performed in a multi-step process proceeding from a MD simulation using the Unified Forcefield (UFF) model,⁵⁴ followed by DFT optimisation with a heterogeneous basis set⁵⁵ (def2-SVP on nonmetal atoms, and def2-TZVP on metal atoms) and variable SCF and grid precisions that are adjusted to obtain convergence in the potential energy gradient. Unless otherwise indicated, high-quality geometry convergence was obtained to a BP86/def2-TZVP/D3BJ level of theory on all atoms, with an SCF convergence criterion of ≤1 × 10⁻⁹E_h and numerical grid quality settings of at least Grid3 and FinalGrid5. Calculations using heterogeneous basis sets retain these settings but substitute a 6-31G* basis on designated atoms. Final geometries are converged to the default criteria of ORCA (ΔE: ≤5 × 10⁻⁶E_h, ∇E_RMS: ≤1 × 10⁻⁴E_h·a₀⁻¹, ∇E_max: ≤3 × 10⁻⁴E_h·a₀⁻¹, Δr⃑_RMS: ≤2 × 10⁻³a₀, Δr⃑_max: ≤4 × 10⁻³a₀).

Gaussian integrals are calculated by the LIBINT library.⁵⁶ The def2/J auxiliary basis was used for the Split-RI-J approximation.⁵⁷ Where calculations are solvent corrected, the CPCM continuum approximation with preset parameters for water (ε = 80.4 D (2.682 × 10⁻²⁸ C m⁻¹), n = 1.33) used, alongside the SMD augmentation of Marenich, Cramer, and Truhlar.⁵⁸ Intrinsic bond strength index⁵⁹ analysis (IBSI) was performed using MultiWfn.⁶⁰

Initial construction of molecular models was undertaken using the SAMSON and Avogadro programs.^61,62 Structural visualisation was achieved using the PyMOL molecular graphics suite v2.2.0⁶³ and the Blender 3D graphics program.

2.2 Graphene model

Pristine EFG may provide a large number of micro-environments based on both the edge functionalisation pattern and the structure of the incipient graphene lattice. An idealised, straight-edged graphene sheet can provide two different edge geometries (so-called ‘armchair’ and ‘zig-zag’ edges) with differing periodic lengths and derived functionalisation geometries. Less regular edge structures (which we will term ‘ragged’ offer more possibilities, including two-dimensional prominences and pockets). These terms are illustrated in Fig. 3.

Fig. 3 (a) Depiction of ‘zig-zag’ and ‘armchair’ edge types in idealised graphene sheet. (b) Depiction of ‘ragged’ graphene sheet exhibiting a range of micro-environments. Both structures were obtained by UFF geometry optimisation.

To constrain the large number of potential coordination geometries, in the present work we consider bi-functionalisation of a zig-zag edge.

2.3 Criteria for model Mn_xO_y species

Manganese oxide clusters of even low nuclearity possess a very high combinatoric complexity in their number of potential configurations of the cluster oxomanganese skeleton, bridging ligands, protonation states, oxidation states, and Jahn–Teller activities. Candidate manganese oxide clusters in the present study are constrained by the geometry of salient carboxylate ligands reasonably possessed by an EFG sheet. Four additional constraints are employed to reduce the list of clusters considered for simulation. These are (a) cluster nuclearity ≤4, (b) high symmetry, (c) termination by water and/or hydroxide ligands, and (d) bridging ligands of order ≤3. Five Mn_xO_y clusters with unique connectivity graphs satisfying the aforementioned constraints were shortlisted for investigation, however, in the present study we limit our analysis to three of these, selected for compatibility with bidentate ligation to a zig-zag graphene edge and similarity to both the PSII OEC active site substructures of laminar oxo-manganese minerals with putative water oxidising activity. Two of these structures are different attachment configurations of the concatenated hemicubane structure (ch) and the third is the cubane (cu) structure indicated in in Fig. 4.

Fig. 4 Mn_xO_y substructures shortlisted for investigation. The number and type of bridging ligands for each substructure is indicated, with μ₂ denoting a two-coordinate bridging oxo ligand, and μ₃ denoting a three-coordinate oxo cap.

3 Results

3.1 Intrinsic flexibility of graphene sheet

As previously established, graphene is a highly flexible material that is capable of high local curvatures, stabilised by van der Waals self-interaction. This suggests that chelation of TMO clusters or nanoparticles by EFG may involve flexion of the graphene edge, however such effects are computationally expensive to systematically explore at a DFT level of theory. The strain energy associated with folding and twisting a graphene sheet at the chosen level of theory was modelled by deformation of a pair of rectangular graphene nanosheets and distinguished by whether their long edges possess the armchair or zig-zag structure. The edges of each sheet are saturated with hydrogen atoms. The bending of each sheet was effected by varying the distance d between two carbon atoms at opposite short edges of the sheet. Helical torsion was applied to the sheet by varying the dihedral angle of the corners of the sheet between 0 and 60° in 5° increments.

The radius of curvature of the sheet is estimated as the radius of the circumcircle defined by the positions of the indicated edge carbon atoms and the centroid of the central aromatic ring of the sheet. The radius r_c is related to the vectors connecting the edge atoms to the ring centroid a and b by the formula given in eqn (1). Whilst the graphene sheet model deviates from strict conformation to a cylindrical section, we posit the described curvature measure to be an acceptable first-order approximation. The helical pitch p of a graphene sheet undergoing twisting deformation is the extrapolated sheet length required to achieve a full rotation at the nominal twist angle.

The strain energy induced in the graphene nanosheet by the radius of curvature r_c and helical pitch p of the sheet is illustrated in Fig. 5. The strain energy associated with bending deformations (Fig. 5a) is appropriately approximated (R² = 0.997) by the functional form , where a has a best-fit value of approximately 1.26 × 10² kJ nm² mol⁻¹. We note that modelling the graphene sheet as a deflected beam indicates that the sheet has nonlinear elasticity. The strain energy associated with twisting deformations along the armchair axis (Fig. 5b) is appropriately approximated (R² = 0.999) by the functional form , where a is approximately 7.54 × 10⁴ kJ nm³ mol⁻¹. However, helical deformation of a sheet along the zig-zag direction is approximated (R² > 0.999) by the functional form , where a is approximately 8.43 × 10³ kJ nm² mol⁻¹. It should be noted that the relative energy associated with deformations of each graphene sheet is an extensive quantity, and therefore the zig-zag and armchair nanosheets are not directly comparable. Nevertheless, these data demonstrate that the energies associated with out-of-plane deformations of zig-zag and armchair edges are of the same order of magnitude, and that they are adequately characterised by simple functional forms.

Fig. 5 Plots of relative strain energy of folded and twisted graphene nanosheets with respect to approximate radius of curvature and helical pitch. Folding is achieved by nonlinear transit of separation d between edge carbons indicated with blue markers. Twisting is achieved by transit of dihedral angle constraint for the indicated atoms. Inset left: Exemplary sheet geometries at differing radii of curvature. Inset right: Exemplary sheet geometry at twist angle of 60°.

These data indicate that non-negligible distortions of graphene fragments are accessible at low energies, however the corresponding strain energy rapidly increases below a radius of curvature of less than approximately 2 nm, or a helical pitch of less than 25 nm. At large deflections, a small negative Gaussian curvature (i.e. a ‘saddle’ curvature) is developed in the sheet. This curvature is likely to be due to the limitation that the transit constraint which has been applied only constrains three atoms lying along the centreline of the sheet.

3.2 Concatenated hemicubane models

The concatenated hemicubane structure (ch) can be interpreted as a minimal capped fragment of a birnessite (MnO₂) sheet (or other laminar metal oxide with a 1T lattice structure). Birnessite has been identified as a water oxidation catalyst.⁶⁴ Indeed, the ultimate active form of the Mn₄O₄ cubane catalyst⁶⁵ of Dismukes, et al.—which alongside the PSII OEC serves as structural inspiration for the cu model—has been proposed as a variety birnessite based on EXAFS evidence.⁶⁶ The birnessite structure is composed of face-sharing MnO₆ octahedra. As such, the surfaces presented on either side of the lamina are entirely composed of μ₃-oxo caps, and all interior Mn ions are coordinatively saturated. Therefore, covalent coordination of Mn ions in birnessite can only take place at defect sites (e.g. oxygen vacancies, Rütschi defects) or at the edges of MnO₂ laminae. The ch skeleton is an attractive structure for study not only as a potential water oxidation catalyst precursor, but also as a plausible substructure of an EFG-attached birnessite nanoparticle.

We explored two potential coordination modes of the minimal ch skeleton to EFG. These modes are denoted ch-tall and ch-wide. These clusters differ in the coordination of the EFG simulant carboxylate ligands. Their attachment to a notional EFG sheet via two colocated carboxylate ligands is illustrated in Fig. 6. ch-tall and ch-wide have equivalent ligand sets and therefore can be usefully considered to be related by an isodesmic transformation. Where ligation of an extended birnessite sheet to EFG is considered, a functionally infinite variety of coordination modes exist. These include bridging of multiple graphene sheets by a single birnessite sheet, coordination involving defective structures, or coordination geometries relying upon long-range warping of graphene and/or birnessite sheets. These possibilities are not amenable to the form of electronic structure analysis undertaken here for reasons of combinatoric complexity and computational expense.

Fig. 6 (a and b) Schematic depiction of possible κ²:κ² bis(carboxylato) coordination modes to the ch skeleton. (c) Illustration of minimal monopodal nucleation of MnO₂ nanosheet from single carboxylate ligand. (d) Illustration of polypodal nucleation of MnO₂ nanosheet from multiple potentially discontiguous attachment points.

3.2.1 Concatenated hemicubane isomer geometries. The ch-tall isomer possesses quasi-C_s symmetry. This complex is depicted in Fig. 7a. The ch-tall isomer possesses an Mn^IV oxidation state configuration on all Mn ions (confirmed via Mulliken population analysis), however lower oxidation states are in principle accessible through protonation of OH⁻ or O²⁻ ligands. In light of the oxidation state distribution of the molecule, no Jahn–Teller axes exist.

Fig. 7 (a and b) Complex based on ch-tall oxomanganese skeleton, viewed from two different angles. Complex has quasi-C_s symmetry. The laminar, birnessite-like structure of the fragment is apparent when the complex is viewed from the side. (c and d) Complex based on ch-wide oxomanganese skeleton, viewed from two azimuthal angles. Complex has quasi-C₂ symmetry. Both depicted structures computed at a RI-BP86/(def2-TZVP/def2/J)/D3BJ level of theory.

The ch-wide isomer possesses quasi-C₂ symmetry. The ch skeletal geometry prevents collinear coordination of κ²:κ²-carboxylato ligands to the same side of the cluster, however it is presumed that the rotational degrees of freedom of the 4-formamidobenzoic acid moieties attached to an EFG sheet, as well as coordinative micro-environments created by ragged graphene edges, will comfortably accommodate the coordination geometry enforced by the oxomanganese cluster.

The ch-wide isomer possesses an implicit Mn^IV oxidation state configuration on all Mn ions (confirmed via Mulliken spin population analysis) equivalent to ch-tall. All waters exist as aqua ligands (Mn–O: 211 ± 3 pm), and a symmetric hydrogen bonding network exists between the aqua, hydroxo, and two μ₂-oxo ligands. The obtained geometry is depicted in Fig. 7b.

The gas phase and solvent corrected geometries of ch-wide are virtually identical, however the hydrogen bonding network previously described is erased. The aqua ligands are deactivated to 204 ± 0 pm and proton reorientations occur which break hydrogen bonding with both the μ₂-oxo and hydroxo ligands.

3.2.2 Comparison of concatenated hemicubane isomers. As previously indicated, the two concatenated hemicubane isomers are related by an isodesmic transformation, and therefore their binding energies can be directly compared. ch-tall is stabilised by approximately 75 kJ mol⁻¹ with respect to ch-wide in the gas phase, which decreases to 37 kJ mol⁻¹ upon solvent correction. These structures are not guaranteed to be the lowest energy conformations, and ch-tall is notably not stabilised by a hydrogen bonding network (although limited hydrogen bonding is in principle possible). These data suggest that nucleation of a birnessite nanoparticle from a ch-tall configuration is mildly energetically favoured.

3.3 Cubane (cu) model

The cubane model consists of a Mn₄O₄ cluster with similar coordination geometry to the ch-tall model, however each Mn ion in this complex is in the +3 oxidation state, and hence each ion expresses a Jahn–Teller axis of elongation. This cluster is illustrated in Fig. 8d and 10. The Mn_c ion most distal from the coordinating carboxylate ligands is coordinated by a neutral κ³-triazacyclononane (TACN) ligand, whilst the coordination spheres of all other Mn ions are completed by aqua and hydroxo ligands. In practice, cooperativity between the Jahn–Teller activation of Mn_O bonds and the ligand hydrogen bonding network leads to deligation of an aqua ligand. Similarly labile behaviour is a common feature of solvated models of Jahn–Teller active Mn_xO_y clusters with aqua and hydroxo ligands.

Fig. 8 Prototypical graphene-consistent ligand constraint of ch-wide oxomanganese cluster. Nonpolar protons are hidden for clarity. (a) Side angle, illustrating coordination of ch-wide fragment by 4-(2-methylprop-2-enamido)benzoate (PMPAB) ligands simulating edge-functionalised graphene with a separation of 4 rings. Cartesian constraints are indicated with yellow balls marked with +. (b) The same structure viewed edge-on. (c) ch-tall model with graphene-consistent ligand constraints, simulating a separation of 4 rings by coordination to pinned 3-(2-methylprop-2-enamido)benzoate (MMPAB). (d) cu model with analogous graphene-consistent ligand constraints.

In all three clusters, structural perturbations imposed by solvent correction consisted of minor reorientations of terminal ligands. Therefore, we opted to compute further model calculations in the gas phase. Intrinsic bond strength index (IBSI) analysis (see ESI†) of the ch-wide and ch-tall clusters indicate that Mn-aqua bonds in these complexes are exceptionally weak (competitive with hydrogen bonds), and therefore these reorientations are interpreted as low-energy phenomena.

3.3.1 Graphene-consistent ligand constraint results. The graphene-consistent ligand constraint (GCLC) approach involves simulation of a free graphene sheet from which credible attachment points for an oxo-metal cluster are identified. These attachment points are abstracted as the terminal propenyl moiety of 3- and 4-(2-methylprop-2-enamido)benzoate (MMPAB/PMPAB) ligands, mimicking edge functionalisation of the graphene sheet. Such a propenyl moiety will be henceforth referred to as a ‘pin’ for reasons of concision. Rigid geometric constraints were applied to these pins, consistent with the equilibrium edge geometry of the free graphene sheet. Pin separations consistent with the graphene ‘zig-zag’ edge were determined to be 246 pm apart. We discuss alternative models for attachment of clusters to the graphene edge, why these approaches were not adopted, and the derivation of the pin separation distance detailed in the ESI.† Optimisation of ch-wide, ch-tall, and cu models using constraints derived from the graphene structure previously obtained obtain credible attachment geometries for each oxo-manganese cluster. The ch-wide model is depicted in Fig. 8, and considers symmetric coordination of the cluster by two μ₁:μ₁-PMPAB ligands separated by four phenyl rings. Over the course of optimisation, a tautomerisation of the cluster took place, with a proton being transferred from one of the aqua ligands originally attached to Mn_c onto a hydroxo ligand attached to Mn_b, which accounts for the presence of two aqua ligands on Mn_b. The facile nature of this proton transfer suggests that such transfers may occur readily in the hydration environment of birnessite-like oxomanganese cluster edges. This loss of connective symmetry is unlikely to be relevant to the conformational analysis.

EFG attachment of the ch-tall and cu models is simulated by the use of μ₁:μ₁-MMPAB ligands. These alternative EFG ligands are required to obtain approximately collinear terminal propenyl moieties compatible with graphene attachment. Whereas the EFG simulant ligands and oxo-manganese cluster of the ch-wide model are essentially coplanar, the ch-tall and cu models lie out of plane with the graphene-consistent ligand constraints.

3.4 Linear transit of attachment geometries

Linear transit was employed to establish the potential energy surface associated with differing attachment points of the cluster to the graphene ‘zig-zag’ edge, distinguished by different numbers of intervening phenyl rings between the attachment points (between 2 and 6 rings). The computational procedure adopted involves increasing and decreasing the distance between pins in 49.2 pm increments (i.e. 246 pm divided by 5). These interpolating geometries are necessary to obtain SCF convergence, and also provide information about plausible energetics for cluster attachment to deformed graphene sheets.

The potential energy surfaces associated with linear transit of the ligand constraints for models ch-wide, ch-tall, and cu are depicted in Fig. 9. These transits reveal that the most energetically favourable attachment geometry in each case has an edge functionalisation separation of four phenyl rings, which comports with the initial ‘guess’ geometries which were constructed (depicted in Fig. 9). The potential energy surface of each linear transit (prior to any bond rearrangement) is adequately (R² = 0.85–0.99) described by a quadratic model which indicates that the elasticity of each cluster is quasi-Hookean over this domain (k ≈ 385–503 kJ nm⁻²). Data relating to these quadratic fits (as well as corresponding mixed-basis models) are presented in the ESI.†

Fig. 9 Potential energy surfaces for linear transit of EFG simulant pinning distances (black). Interligand separations consistent with the periodic structure of the graphene ‘zig-zag’ edge are indicated with black circles, annotated by the equivalent number of phenyl rings separating the ligands. Potential energy surface of relaxation of pinning constraints from a separation of 1.232 nm (consistent with a separation of four phenyl rings) is indicated in blue. Equilibrium geometry of unpinned structure is indicated with blue circle. A parabolic fit in three variables (E = v₀(x + v₁)² + v₂) to the linear transit energies is indicated in pink. n.b. in each case, analogous linear transits using heterogeneous basis sets (consistent with the partitioning scheme indicated in Fig. 13) are underlaid in faded colours, however in the case of the ch-tall and cu models these potential energy surfaces are substantially occluded due to their close similarity to the homogeneous basis results.

These data indicate a modest degree of flexibility in permissible EFG coordination of each cluster. However, ch-tall and cu models reveal somewhat lower compatibility with high pin separations: the energy associated with linear transit of both models become non-monotonic, and this is explained in both models by the breakage of a bond between Mn_a and a MMPAB ligand. In the case of the cu model, bond breakage and internal rearrangement of a aqua ligand to participate in hydrogen bonding with the deligated oxygen of a nascent monodentate MMPAB ligand is noted (Fig. 10). This configuration surprisingly obtains a lower total interaction energy than either the four-ring separated structure or the unconstrained structure (−20 kJ mol⁻¹ with respect to unconstrained structure) and is suggestive of additional potentially catalytically significant coordination modes for molecular oxo-manganese clusters, however exploration of these modes is beyond the scope of this manuscript.

Fig. 10 Internal rearrangement of cu model (homogeneous basis) at maximum pin elongation (1.72 nm). Mn_a has become coordinatively unsaturated (a), and W₁ has reoriented to engage with hydrogen bonding with the deligated oxygen of the indicated MMPAB ligand (b).

Partial release of the constraints applied to each model (i.e. the internal constraints of each pin were maintained, however the pins were allowed to move with respect to one another) depicted in Fig. 8 establishes an estimate of the conformational strain of attachment of ΔE ≤ 20 kJ mol⁻¹ (the blue branches of Fig. 9). These data indicate that the ch-wide ligands are placed under compression at a four-ring separation, whilst the other two models are placed under tension.

3.5 Conformational strain of ligand/graphene dihedral angle

The edge-functionalisation of graphene by amide linkage is liable to result in sterically hindered ligands, due to steric clashes between the amide proton and carboxylate oxygen of the ligand and the salient protons of the graphene sheet. A linear transit of the 4-formamidobenzoic acid ligand dihedral from −90° to 90° with respect to a graphene fragment was undertaken to investigate the energetics of this steric clash, the results of which are depicted in Fig. 11. These data reveal a 23 kJ mol⁻¹ barrier to achieving a coplanar configuration of the ligand amide moiety with the graphene sheet, however substantial deformation of the zig-zag edge occurs due to the steric clash. The ligand dihedral may be rotated in a sterically clashed state by a further 35° before the clash is resolved and the graphene sheet reacquires a quasi-planar configuration, with a 49 kJ mol⁻¹ barrier to complete rotation. The potential energy surface of this transit is markedly asymmetric due to the path-dependence of the geometry in that region. Transit of the dihedral angle from the opposite direction would be expected to yield a mirror image of the obtained potential energy surface, by symmetry. These data indicate that dihedral angles deflected by approximately 50° from coplanarity with the graphene sheet are favoured for EFG achieved by amide linkage, plausibly attributable to a balance of weak resonance stabilisation and the aforementioned steric collision. Outside of the periplanar region, essentially unhindered rotation of the EFG ligand is permitted.

Fig. 11 Linear transit of dihedral angle of EFG model. The dihedral is defined in terms of the illustrated atoms marked with yellow balls. Graphenic and phenyl protons not relevant to steric interactions have been hidden for clarity.

3.6 Distortion of oxo-manganese cluster by coordination environment

Measurement of the core geometry of the ch-wide model as a function of the linear transit coordinate indicates that the internal structure of the oxo-manganese cluster is remarkably insensitive to the large changes in coordination geometry seen over the course of the linear transit. These data indicate an approximately linear relationship between increase or decrease of the pinning distance of the EFG simulant and the maximum absolute deviation and RMS deviation of all Mn–O bond lengths in the cluster, with respect to the 4 phenyl ring separation equilibrium state. The mean deviation in the core geometry across the linear transit is negligible. Moreover, the distortion of the oxo-manganese core is dominated by elongation and contraction of the metal–carboxylate bonds between the benzoate moieties of the EFG simulant and the Mn ions of the cluster. When this is neglected, the oxo-manganese cluster and its remaining ligands are essentially structurally invariant over the course of the transit. These data are illustrated in Fig. 12. Moreover, the core geometry is also negligibly perturbed by release of the pinning constraints (RMSD discrepancy 0.25 pm, maximum discrepancy 0.52 pm), affirming that structural investigations of the oxo-manganese core may be made without applying graphene-consistent ligand constraints.

Fig. 12 Maximum absolute error and mean error in oxo-manganese core geometry of ch-wide as a function of pin separation, normalised with respect to a pin separation of 1.232 nm, consistent with an EFG attachment separation of 4 phenyl rings. The ‘full’ geometry is defined as all of the manganese–oxygen bond distances in the molecule (including aqua/hydroxo ligands). The ‘core’ geometry is the full geometry, minus carboxylate oxygens.

3.7 Comparison with integrated models

Obtaining electronic structures for integrated graphene/oxo-manganese cluster complexes is very difficult due to the exceptional complexity of SCF convergence in such models. Nevertheless, structures corresponding to coordination of ch-wide to the zig-zag edge of a graphene nanosheet were obtained for 3, 4, and 5 ring interligand separations, and a corresponding ch-tall model was obtained with a 4-ring separation. These structures require a lower-quality (6-31G*) basis set on the graphene nanosheet and non-carboxylate ligand atoms to obtain SCF convergence. An illustrative subset of these structures, as well as the basis set partitioning scheme used, are illustrated in Fig. 13. The results of these calculations reveal a remarkable similarity with structures obtained under the graphene-consistent ligand constraints previously enumerated. In each instance, coordination of the ch-wide cluster to the graphene edge induces a helical deformation in the sheet, however the deviation from planarity is quite small, and therefore the helical pitches associated with these distortions are exceptionally long (157 to 280 nm).

Fig. 13 Graphene-integrated cluster models, derived from the ch-wide cluster. (a) ch-wide at a 4-ring attachment point distance. (b) The same, at 3 rings. (c) The same, at 5 rings. Not shown: ch-tall derived model at a 4-ring separation, ch-wide derived isodesmic series at 3-5 ring separation, based on the 5-ring model shown in (c).

We hypothesised that—because the geometry of the cluster represents a balance of forces—the independent conformational energies arising from flexion in the graphene sheet and compression or tension of the cluster would be approximately equal. Our hypothesis is not borne out by conformational analysis of the separated components of the complex: folding and helical deformations of the graphene sheet (estimated by consistent angular/dihedral constraints on separated graphene nanosheets) are of a substantially lower energy than the total conformational energy of the attached cluster. Rather, the energy of relaxation of the ch-wide fragment is −44 kJ mol⁻¹, whilst the energy of relaxation of the graphene nanosheet fragment is −8 kJ mol⁻¹. Of this, the energy attributable to the helical distortion of the graphene nanosheet is approximately 0.1 kJ mol⁻¹. As such, approximately 35 kJ mol⁻¹ arises from interactions between the fragments, plausibly consisting of a combination of steric and π···π interactions between the graphene sheet edge and the PMPAB ligands. Further exploring the decomposition of conformational factors in the energy of attachment of the ch-tall cluster to the graphene nanosheet, we find that the conformational energy of the large-scale sheet deformation seen—whilst more substantial than that of ch-wide—is only 1.2 kJ mol⁻¹. Therefore, we propose the following conformational energy decomposition of cluster chelation:

E^clus_tot. = E^clus_steric + E^clus_pin + E^sheet

where E^clus_tot. is the total conformational energy of the cluster, E^clus_steric is the contribution to the energy arising from steric clashes between the salient protons of the graphene sheet and the amide linkage of the connecting ligands, E^clus_pin is the energy arising from the compression or tension developed in the cluster by the constraint of the graphene edge, and E^sheet is the (small) nonlocal deformation energy of the graphene nanosheet. These data are provided in Table 2. Localised deformations of the nanosheet due to steric interactions are not separable from E^clus_steric. These energies are obtained by extracting clusters of equivalent nuclearity to the GCLC models from each integrated model, saturating to obtain PMPAB/MMPAB ligands, and progressively partially optimising their geometries. E^clus_tot. is obtained by optimising the terminal propenyl proton positions whilst constraining all other atomic coordinates. E^clus_steric is obtained as the difference in energy upon relaxing all atomic coordinates except for the terminal propenyl carbons of the ligands, which are held at the same coordinates as in the integrated model. E^clus_pin is obtained as the difference in energy between E^clus_steric and further relaxation in which the internal geometry of the carbons of each propenyl moiety are constrained but the moieties are allowed to move with respect to one another. Further details of this decomposition scheme are provided in the ESI.†

Table 2 Conformational energy decomposition of ch-wide and ch-tall graphene-integrated models at a 4-ring separation, in comparison with GCLC models. GCLC models do not contain the steric component (E^clus_steric) of the integrated models

Model	Conformational energy (kJ mol^−1)
		Cluster sterics	Cluster pinning
	Total	Integrated model	Integrated model	GCLC	Error
ch-wide	43.7	19.7	24.0	19.6	4.4
ch-tall	20.4	15.0	5.4	5.4	0.0

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We find that the GCLC pinning energy is remarkably consistent (ΔE ≤ 4.4 kJ mol⁻¹) with that obtained by decomposition of the integrated model. However, steric interactions are a significant contributor to the total conformational energy, and these are not captured by GCLC models. Nevertheless, comparison of the relative energies and interligand distances of graphene-integrated ch-wide clusters at 3–5 rings of separation (achieved as an isodesmic series) with the corresponding GCLC models obtains an extraordinary level of agreement (ΔE ≤ 1.3 kJ mol⁻¹, Δ_dist ≤ 9 pm) over this domain (Table 3), which implies that E^clus_steric is markedly insensitive to ligand separation, and that neglecting this contribution to the E^clus_tot. is an appropriate approximation and may also hold for similar ligands and interligand separations. Based on the recovered E^clus_steric energy of ch-wide at a 4-ring separation (Table 2), a tentative steric contribution of approximately 20 kJ mol⁻¹ (i.e. 10 kJ mol⁻¹ per PMPAB ligand) may be assigned. Attempts to produce a simple functional model of the steric energy associated with a deformed PMPAB ligand in two dihedral parameters proved unsatisfactory, only recovering approximately half of the expected energy, suggesting that the steric contribution to the energy is the result of many geometric parameters of small individual effect. These efforts are discussed in the ESI.†

Distortion of the graphene sheets by attachment of the ch-wide and ch-tall clusters was found to be surprisingly mild. Least-squares structural alignment of relaxed and constrained graphene sheets extracted from ch-wide and ch-tall integrated models (4-ring separation) were performed on carbon atoms using the align function in PyMOL with default settings. These alignments reveal a negligible (Δ_min = 0.6 pm, Δ_max = 16.16 pm, Δ_mean = 5.3 ± 3.8 pm) helical distortion in the ch-wide isomer and a moderate (Δ_min = 0.7 pm, Δ_max = 43.6 pm, Δ_mean = 11.5 ± 9.9 pm) localised fold distortion in the ch-tall isomer. The absolute displacements of the carbon atoms of each sheet are illustrated in Fig. 14, and essentially capture out-of-plane distortions. These distortions are almost certainly overestimated by the finite graphene nanosheet model, because the peripheral carbons of the sheet are likely to have greater conformational freedom than the corresponding carbons in an infinite graphene sheet. Rather, in infinite or much larger graphene sheets, distortions induced by edge attachment of clusters are expected to attenuate over very short distances.

Fig. 14 Absolute distortion of graphene nanosheets from relaxed carbon positions induced by coordination of ch-wide and ch-tall clusters at 4 ring separations. Attachment points of PMPAB/MMPAB ligands are indicated with +. Graphene nanosheet binding ch-tall cluster is deflected away from the cluster.

Table 3 Comparison of interligand separations and relative energies of ch-wide graphene-integrated and GCLC models

Ring sep.	Interligand distance (nm)			Relative energy (kJ mol^−1)
	Integrated model	GCLC	Error	Integrated model	GCLC	Error
3	0.995	0.986	−0.009	22.7	23.9	+1.2
4	1.240	1.232	−0.008	0.0	0.0	—
5	1.479	1.478	−0.001	5.6	6.9	+1.3

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Core geometries of graphene-integrated clusters are essentially unperturbed with respect to GCLC models, to the point of visual indistinguishability (maximum core bond length discrepancy ≤1 pm, maximum core RMSD displacement (all-atom) of 2.4 pm). These data are consistent with earlier core distortion results (Section 3.6) and indicate that the cluster core geometry is insensitive to both the steric influence of the graphene sheet upon the ligands, and hypothetical electronic coupling between the oxo-manganese cluster and the graphene sheet intermediated through the amidobenzoate ligand.

4 Discussion

4.1 Utility of structural models

The structural models presented in this report are notional, as the disposition of graphene edge functionalisation and TMO nanoparticles is a function of a large number of variables. Particularly, it is not known whether catalytically active sites will be in the form of molecular clusters of low nuclearity such as those demonstrated herein, or in the form of nanoscale/microscale periodic structures generated through edge-attached nucleation sites. Analytic techniques such as SEM, HRTEM, and/or EXAFS are likely to shed significant light on the nature of EFG-attached catalytic particles in situ.

The clusters demonstrated in this work nevertheless represent useful limiting cases for incipient crystal growth from EFG, and thereby afford information on how such crystals may be attached to-and perturbed by-EFG.

4.2 EFG is anticipated to flexibly bind oxo-manganese clusters

This work has demonstrated a number of coordination geometries consistent with the ligation environment provided by edge functionalisation of a rigid, linear graphene edge are capable of chelating a compact oxo-manganese cluster at two points. It is likely that EFG will provide a massive number of geometrically distinct ligand sets capable of coordinating oxo-manganese clusters on account of the large number of degrees of freedom of the EFG ligands and the underlying graphene sheet they are attached to.

4.3 Oxo-manganese clusters are anticipated to be very structurally insensitive to EFG coordination

Linear transit investigation has revealed that the birnessite-like oxo-manganese cluster ch-wide is insensitive to significant shifts in EFG simulant pinning distance (spanning 0.984 nm). This observation suggests that oxo-manganese clusters in general are plausibly much more rigid than the coordinating ligands provided by EFG, and that structural perturbations of oxo-manganese clusters imposed by EFG coordination are sufficiently small that they may be neglected from models. However, at extreme pinning distances fundamental incompatibility of the ligation environment resulted in dismemberment of the ch-tall and ch-wide cluster, with partial deligation of a μ₁:μ₁-MMPAB ligand to the corresponding monodentate species and internal rearrangement of the oxo-manganese core, indicating that a degree of caution should be taken in establishing a reasonable domain in which ligand effects may be neglected for a novel cluster or ligand set.

4.4 Graphene-consistent ligand constraints are anticipated to be a suitable approximation of explicit graphene coordination

We have found that GCLC models preserve important features of their corresponding integrated models, including excellent maintenance of the oxo-manganese core geometry and the relative energetics of interligand separation. We have performed analysis of the conformational deformations imposed by cluster attachment to a graphene sheet and have determined that the majority of this deformation is in the form of steric clashes between the graphene nanosheet edge and ligand amide moiety, and that this steric component of the conformational energy is implied to be an approximately constant factor over the species investigated. Surprisingly, in spite of the flexibility of graphene, bulk deformations of the graphene nanosheet due to cluster attachment are vanishingly small.

5 Conclusions

Herein, we have illustrated a number of case studies modelling the connection of low-nuclearity Mn_xO_y clusters to graphene edges. Whereas explicit modelling of such clusters attached to graphene nanosheet fragments is extremely computationally expensive, we have developed a methodology which probes the conformational energetics of oxo-manganese cluster deformation and graphene edge deformation as separable problems, without significant loss of fidelity. This approach greatly simplifies modelling of proposed EFG/oxo-manganese composites.

The calculations presented here are of practical relevance to the creation of manganese oxide/graphene composite materials because they indicate that covalent chelation of Mn_xO_y clusters by edge-functionalised graphene is a low-energy proposition, even where the linking moiety is compact and quasi-rigid. These results strongly indicate that edge-functionalised graphene is capable of forming robust associations with Mn_xO_y particles without disruption of the electronic properties of the graphene sheet interior. The degrees of conformational freedom revealed by this work are therefore anticipated to guide the rational design of linking ligands for the covalent coupling of graphene edges to transition metal oxides in a generic sense. On account of the flexibility seen here, an outstanding question is whether linking ligands are strictly necessary to effect coordination of TMO clusters, or whether carboxylate moieties obtained by oxidation of graphene edges are intrinsically capable of TMO coordination.

Calculations modelling small-scale deformations of graphene edges reveal a modest flexibility in out-of-plane bending and helical torsion which we anticipate will reduce the energetic barrier to coordination. As such, the potential energy surfaces we have obtained represent a limiting ‘worst case’ scenario. In spite of this constraint, linear transit of the ch-wide model indicates compatibility with a number of graphene edge consistent coordination geometries.

We note that the ch-wide model core geometry is nearly totally insensitive to applied intramolecular torques consistent with strained chelation geometries. This fact strongly suggests that geometric effects in oxo-manganese clusters arising from polydentate chelation at an EFG edge may be freely neglected in energetically plausible cases. The ch-wide geometry offers a rich array of proximately located H₂O and OH⁻ ligands singly ligated to Mn atoms, which suggests potential importance to water splitting function, which is a target for future investigations. However, sufficiently elongated inter-pin separations were found to induce carboxylate–Mn bond scission in the ch-tall and cu cluster models.

Actually existing graphene edges are commonly ragged and therefore possess a large number of geometric micro-environments which may fortuitously support edge functionalisation and chelation of manganese oxide particles. This, combined with possibility of large-scale deformations of graphene sheets and inter-sheet coordination, comprise a nearly unrestricted set of geometries and topologies for cluster attachment and nanoparticle/sheet nucleation at EFG. The investigation of these possibilities is likely to defy electronic structure methods for the foreseeable future. Nevertheless, TMO chelation at closely-spaced edge functionalities represents a high-density scenario for molecular TMO attachment and is presently amenable to DFT methods, permitting some useful bounds to be assigned to the geometric configuration space of such clusters. Contrariwise, monodentate attachment of TMOs to EFG is plausibly only constrained by the steric interactions between the EFG ligand and the graphene edge. We have investigated this for a realistic EFG ligand and found high rotational freedom outside of the periplanar region.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The amidobenzoate graphene edge functionalisation environment underpinning the computational models in this work is based on synthetic work performed by Dr Danijel Boskovic, which we gratefully acknowledge. This work was financially supported by the Australian Renewable Energy Agency (ARENA), contract number 2018/RND004. This activity received funding from ARENA as part of ARENA's Research and Development Program-Renewable Hydrogen for Export. The views expressed herein are not necessarily the views of the Australian Government and the Australian Government does not accept responsibility for any information or advice contained herein. This research was undertaken with the assistance of resources from the National Computational Infrastructure (NCI Australia), an NCRIS enabled capability supported by the Australian Government.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cp04178e

‡ n.b. that the surface area of preparations of bulk graphene may be considerably lower than this value and highly variable, as established by Brunauer–Emmett–Teller (BET) assays of reduced graphene oxides (rGO).^4,5

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